U.S. patent number 5,646,623 [Application Number 06/324,677] was granted by the patent office on 1997-07-08 for coherent, frequency multiplexed radar.
Invention is credited to Lance M. Teschmacher, Glenn A. Walters.
United States Patent |
5,646,623 |
Walters , et al. |
July 8, 1997 |
Coherent, frequency multiplexed radar
Abstract
Coherent, frequency multiplexed radar is a new generic type of
continuous wave radar architecture wherein contiguous pulses of
discrete frequency segmented signals are serially transmitted from
an antenna, and after reflection from radar targets, signals from
the same antenna are coherently processed in a parallel manner to
provide correlated measurements of target's pulse compressed range
and radial velocity. Simultaneously transmitted and received
signals are separated by frequency multiplexing.
Inventors: |
Walters; Glenn A. (Escondido,
CA), Teschmacher; Lance M. (Del Mar, CA) |
Family
ID: |
26852435 |
Appl.
No.: |
06/324,677 |
Filed: |
November 24, 1981 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
Issue Date |
|
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155592 |
Jun 2, 1980 |
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906049 |
May 15, 1978 |
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Current U.S.
Class: |
342/129; 342/112;
342/200 |
Current CPC
Class: |
G01S
13/32 (20130101); G01S 7/038 (20130101); G01S
13/286 (20130101) |
Current International
Class: |
G01S
13/32 (20060101); G01S 13/00 (20060101); G01S
7/03 (20060101); G01S 13/28 (20060101); G01S
013/536 () |
Field of
Search: |
;343/5NQ,17.2PC,5HM,5BB,9R,14,17.5 ;342/112,129,200 |
References Cited
[Referenced By]
U.S. Patent Documents
Primary Examiner: Barron, Jr.; Gilberto
Parent Case Text
This is a continuation-in-part of application Ser. No. 06/155,592
filed Jun. 2, 1980 abandoned which in turn is a
continuation-in-part of application Ser. No. 05/906,049 filed May
15, 1978 abandoned.
Claims
Having described our invention, we now claim:
1. A continuous wave, frequency-multiplexed radar system,
comprising:
transmitter means for transmitting, against a target, a continuous
output signal having successive cycles, each of said cycles
including N mutually coherent, contiguous segments, wherein said
output signal has a respective predetermined frequency during each
of said segments;
receiver means for receiving a return signal produced by reflection
of said output signal from said target, while said output signal is
being transmitted;
separation means connected to said receiver means for, during each
cycle, separating said return signal into N respective frequency
components corresponding to said predetermined frequencies;
means for successively obtaining quadrature samples from said
separated frequency components for each of the segments of a return
signal cycle, said samples being obtained in a predetermined order
during each of a plurality of range times following transmission of
said signal cycle in said output signal; and
matched filter processing means for combining quadrature samples
obtained from a succession of return signal cycles during a
respective one of said range times to produce indications of the
range and velocity of a target having a range corresponding to said
range time.
2. The system of claim 1 wherein said segment frequencies are
harmonically related.
3. The system of claim 2 wherein said N successive contiguous
segments are pseudo-randomly ordered in each of said output signal
cycles.
4. The system of claim 1 wherein all of the segments of a cycle are
of the same time duration.
5. A method for measurement of target range and velocity by a
continuous wave, frequency-multiplexed radar system including a
transform processing means for combining signal samples to produce
predetermined target indicia, comprising the steps of:
generating a continuous periodic output signal having successive
periods, wherein each of said periods includes N contiguous,
mutually coherent time segments in each of which said output signal
has a respective predetermined frequency;
continuously transmitting said output signal against a remote
target to generate a continuous reflection of said output signal
from said target;
continuously receiving said reflected signal while said output
signal is being transmitted;
separating N frequencies from said received signal;
obtaining quadrature samples from said separated frequencies for
each of the periods of a received signal cycle, said samples being
obtained in a predetermined order during each of a plurality of
range times following transmission of said period in aid output
signal;
for each of said predetermined frequencies, accumulating quadrature
samples obtained from a succession of received signal cycles during
a respective one of said range times; and
combining all quadrature samples accumulated during said range time
to produce indications of the range and velocity of a target having
a range from said radar system corresponding to said range
time.
6. The method of claim 5 wherein the predetermined frequencies of
said cycle time segments are harmonically related.
7. The method of claim 6 wherein time segments are pseudo-randomly
ordered.
8. The method of claim 5 wherein all of said time segments are of
equal duration.
9. A method for measurement of target range and velocity by a
continuous wave, frequency-multiplexed radar system including a
transform processing means for combining signal samples to produce
predetermined target indicia, comprising the steps of:
generating a continuous periodic output signal having successive
periods, wherein each of said periods includes N contiguous,
mutually coherent time segments in each of which said output signal
has a respective predetermined frequency;
continuously transmitting said output signal against a remote
target to generate a continuous reflection of said output signal
from said target;
continuously receiving said reflected signal while said output
signal is being transmitted;
separating N frequencies from said received signal;
obtaining quadrature samples from said separated frequencies for
each of the periods of a received signal cycle, said samples being
obtained in a predetermined order during each of a plurality of
range times following transmission of said period in said output
signal;
for each of said predetermined frequencies, accumulating quadrature
samples obtained from a succession of received signal cycles during
a respective one of said range times;
pulse-compressing the accumulation of quadrature samples for each
of said predetermined frequencies by further sampling each said
sample during each of a plurality of fine range times occurring
during said time;
progressively phase-shifting accumulated, pulse-compressed
quadrature samples obtained during said fine range times and
combining phase-shifted quadrature samples to obtain respective
Doppler frequency accumulations; and
successively combining all of said respective Doppler frequency
accumulations with each of said fine range accumulations to produce
indications of the range and speed of a target having a range from
said radar system corresponding to a respective one of said fine
range times.
Description
BACKGROUND OF THE INVENTION
Radar, since its rapid development during World War II, has become
a primary sensor for both military and nonmilitary operations.
Continuing developments have greatly improved the operational
capabilities of radar systems; however, parallel increases in
operational requirements have increased technological deficiencies.
A relatively large and specialized vocabulary has evolved that
relates to radar problems and operational requirements: e.g.,
clutter, electronic counter measures (ECM), jamming, chaff, decoys,
anti-radiation missiles (ARM), low probability of intercept (LPI),
identification of friend or foe (IFF), electromagnetic interference
or control (EMI/EMC), high density targets, etc. The solutions to
all the above problems relate to improving resolution in the space,
time and frequency domains, and increasing the RF to information
bandwidth ratio. The problems and solutions are interrelated and
are often at cross purposes; e.g., increased resolution often
adversely affects data rates. The development of conventional radar
has been directed towards higher average power, pulse repetition
rates, duty cycles, pulse compression ratios and improved Doppler
frequency resolution. Unfortunately, processing losses associated
with signal eclipsing and functional time sharing along with system
complexity have also increased. A new generic type of radar design
architecture is required. CFMR (coherent frequency multiplexed
radar) offers solutions to many of these categorical problems.
Radar operates in the time, space and frequency domains.
Transmitter and receiver signal isolation can be achieved in any of
these domains. In pulse radar the transmitting and receiving
periods are separated in the time domain. Signal separation in CW
radar systems, except for some special purpose low power
application, is achieved in the space domain (separate antennas).
In CFMR the transmitted wave is continuous, but is comprised of a
series of contiguous pulses transmitted at different frequencies in
such a manner that they can be separated, from each other and from
the signal being transmitted, by frequency multiplex techniques.
Furthermore, a coherent relationship between the voltage vector of
each frequency segment transmitted provides for simultaneous
measurement of target range and velocity with optimum processing
gain maintained.
CFMR is a continuous wave system and must therefore be able to
receive while transmit. It can, in part, utilize the same
implementation as conventional continuous wave radar; primarily,
separate transmitting and receiving antennas, duplexors
(circulators with canceller and Doppler frequency shift. CFMR, by
virtue of its coherent frequency segmented signal format, has the
further advantage of separating the signals through frequency
multiplexing techniques. Foregoing the option of dual antennas for
transmit and receive functions, the duplexor in CFMR operation
reduces the coupling between the transmitter's output and the
receiver's input (radio frequency preamplifier and/or first mixer)
such that the residual transmitted power, as observed at the input
of the receiver, is insufficient to cause burnout, excessive
overloading to introduce undesirable non-linearities or degrade the
receiver's noise figure. In CFMR the frequency separation of
individual segments making up the signal format is accomplished at
IF and/or baseband frequencies through frequency multiplexing by
means of analog filters and/or digital filtering techniques
utilizing appropriate time sampling in the radio frequency
detection process. Doppler extraction is accomplished in much the
same manner as with conventional Doppler radar, i.e., further
dividing coherent baseband frequencies into Doppler frequency
bands. Signal processing is conveniently implemented through
digital computer techniques.
A comparison of the pertinent operational features of the radar
technologies are tabulated below:
__________________________________________________________________________
Resolution Ambiguities Radar Range Velocity Range Velocity
Processing Type (Time) (Doppler Freq) (Time) (Doppler Freq) Gain
__________________________________________________________________________
Pulse or Pulse Doppler ##STR1## ##STR2## ##STR3## ##STR4## ##STR5##
Pulse Compression ##STR6## -- ##STR7## -- ##STR8## Doppler ##STR9##
##STR10## -- none .alpha. T.sub.i' CFMR ##STR11## ##STR12##
##STR13## ##STR14## .alpha. T.sub.i'
__________________________________________________________________________
where c = speed of light f.sub.c = carrier frequency PRF = Pulse
Reception frequency .alpha. = PROPORTIONAL TO T.sub.i = integration
period .tau. = pulse or frequency segment width .tau..sub.e =
1/total bandwidth of transmitted signal
Note brackets 1 and 2. CFMR has the range resolution of pulse
compressed radar and the Doppler resolution of CW radar. Its range
ambiguity, for extended pseudo-random codes, is greater than pulse
by the ratio T.sub.i .multidot.PRF. Its Doppler frequency ambiguity
is 1/.tau., which in practical FFT filter processors is the same
for conventional CW Doppler radars. Coherent processing is used for
both CFMR and Doppler radars and the resulting gain is proportional
to T.sub.i.
The range bin array of coherent signal time elements can be
processed to improve range measurement accuracy and resolution. The
time bandwidth characteristics of the transmitted wave are
efficiently processed. For example, the total accumulated bandwidth
can be utilized in deriving high range resolution. Thus, CFMR
affords the same resolution capabilities as conventional pulse
compressed radar. The period of the range frequency sequence is
usually greater than the transit period to the most distant target
of interest; but can be of any desired length consistent with
scenario geometry and dynamics. This characteristic eliminates
range ambiguities associated with high PRF pulse radars. Continuous
operation provides a 100% duty cycle that minimizes peak power to
an average value. It is the average value of power that determines
radar performance. Non-ambiguous measurements of each target's
range and velocity are simultaneously derived from the same
waveform. These factors extend the capability of synthetic aperture
applications in terms of operating range and ability to efficiently
detect moving targets. This can eliminate the need for large
aperture scanning antennas in radar systems operating from moving
platforms. Furthermore, in fixed installations advantages can be
accrued by utilizing small size, wide angle, transmitting antennas
in combination with large aperture, multi-beam receiving arrays
wherein parallel processing over the total period normally allotted
to scanning a frame provides system gain in excess of the system
loss introduced by the wider angular coverage of the transmitting
antenna. Through parallel processing the data rate is no longer
constrained by scanning requirements, but relates only to scenario
dynamics. A large number of circuit elements are required to
instrument parallel processes. In CFMR the circuits are identical
and repetitive. Available signal processing resources can be used
for wide area, coarse resolution surveillance; sector or restricted
area, medium resolution search or zooming operations for high
resolution target classification.
Conventional radar technology relative to such functions as
sensitivity time control and moving target indications can be
implemented. Advantages of frequency agility, spread spectrum and
frequency related functions are inherent to the process. The
instantaneous bandwidth of each frequency segment is less than that
associated with conventional pulse radars. Peak powers are reduced
to average values and processing losses associated with high duty
cycle, staggered PRF radars are eliminated, thereby minimizing
average power requirements. The segmented signal format allows
maximum use of digital computer technology in terms of time,
frequency, power management, adaptive control and signal
processing. These factors are of prime importance when considering
requirements for covert operation, jamming resistance and other
problems that relate to maintaining operational capabilities in
hostile environments. Improved resolution in the time, frequency
and space domains is the solution to problems related to clutter,
target classification, etc.
SUMMARY OF THE INVENTION
The present invention is a new and unique radar system utilizing a
specific signal format best controlled and processed by special
purpose digital computers and related technology.
The signal format consists of a continuous wave transmission, and
subsequent reception, of a series of discrete frequency segments.
The specific signal format employed can be chosen to provide a
number of functional capabilities. To eliminate range ambiguities,
the code period of the basic signal format is equal to or greater
than the time out to the most distant target of interest. The
frequency steps, within the code period, are sufficiently large to
prevent self-jamming and allow simultaneous transmit and receive
operation from a common antenna through frequency multiplexing
techniques. All frequencies transmitted have a coherent
relationship with the baseband frequency and are generally
harmonically related. The coherent relationship provides maximum
signal processing gain and permits the signal to be pulse
compressed. The continuous wave aspect eliminates PRF velocity
ambiguities and establishes a phase-time schedule of the
transmitted wave form that provides the means for determining
target radial velocity.
Implementing the transmitted signal requires that coherency be
maintained. This is accomplished by establishing a reference or
clock frequency that all other frequencies are coherently related
to. From this reference frequency, a group of harmonically related
baseband frequencies in the video frequency range, can be
coherently derived and then added through mixing with a desired
microwave frequency for serial transmission. Upon reception, the
reflected signals are coherently mixed back down to their original
baseband frequencies, where they are time sampled and processed in
a parallel manner.
Separation of transmitted and received signals from a common
antenna is first accomplished by a circulator. Additional isolation
is provided by cancellation circuitry. This isolation prevents the
residual transmitter signal from damaging, overloading, or
deteriorating the receiver radio frequency pre-amplifier and/or
first mixer circuits. Separation of the signals to individual
baseband frequencies is accomplished within the intermediate
frequency amplifiers and signal detection circuits after the first
mixer.
Frequency demultiplexing requires a frequency separation between
received channels. The greater the frequency separation between
adjacent channels, the less stringent the filtering requirements.
CFMR operation depends upon the transmission of contiguous
frequencies during the range code word to minimize range and
velocity ambiguities. There are a number of design techniques
available to increase the frequency separation between adjacent
time segments while fulfilling the requirements of CFMR operation.
This involves frequency filtering by either analog or equivalent
digital sampling technique in the time domain.
It is generally desirable to weigh the amplitude of the frequency
segments to minimize the time sidelobes in the compressed pulse
pattern. Weighing, without loss in power transfer, can be
accomplished by judiciously omitting the transmission of selected
pulsed frequency segments. Under such conditions all pulsed
frequency segments are transmitted in the central spectral area of
the signal's frequency band while the pulsed frequency segments
nearer the edge of the band are increasingly separated by the
removal of chosen frequency segments. Utilization of nonuniform
frequency segmented codes can be judiciously integrated with other
techniques, such as increasing the frequency separation between
pulses and conserving processing resources.
In CFMR it is not necessary to transmit the frequency segments
making up the total bandwidth required in any particular order.
Several design considerations lead to the conclusion that it is not
desirable to operate in a linearly stepped frequency sequence.
First, the peak sidelobe levels of the ambiguity function and
range/velocity cross-coupling can be minimized for highly non
linear sequences. Second, the code can be made optimum to reduce
effects of harmonic inter-modulation products resulting from the
mixers. Third, an optimum code, or order, can be chosen such that a
maximum frequency separation is achieved between transmitted and
received signals from targets at any desired range, most
importantly maximum range. It is these lower level signals that
determine the maximum isolation requirements. Signals returning
from shorter ranges have greater signal strengths and require less
isolation. Basically, any range at which sensitivity time control
attenuation is used does not require as much isolation between
received signals and the transmitter's leakage power level. The
purpose of the frequency demultiplexer is to retain a required
return signal to transmitter leakage power ratio, generally,
greater than 20 dB.
Baseband frequency components are coherently combined with other
frequencies prior to their final conversion to the transmitter
carrier frequencies for spread spectrum operation. This design
approach may be used advantageously in a CFMR operation where
pre-conversion demultiplexing is used.
The combined choices of the frequency segmented code period and the
bandwidth requirements to provide pulse compressed range resolution
combine to establish the number of frequency segments transmitted
during a given frequency segmented code period. The instantaneous
bandwidth of the transmitted frequency segment is less than the
total bandwidth required to obtain a given range resolution. This
reduction in instantaneous bandwidth coupled with the ability to
utilize arbitrary frequency sequences is of importance when the
desired objective is to operate in a jamming environment or in a
covert manner. The frequency segmented code is normally made longer
than the transit period to the most distant target of interest: to
increase range resolution without increasing the instantaneous
bandwidth, to provide additional jam resistance or covert
operational margins; extend the operational range of synthetic
aperture radar capabilities and reduce the level of "second time
around" targets.
Pulse compression is accomplished by processing the target
reflected frequency segments into parallel time coherency such that
the voltage maximas of each frequency segment can be vectorially
added. The pulse compressed processing gain is proportional to the
number of frequency components so summed. The range resolution of
the compressed pulse is inversely proportional to the total
bandwidth of the processed baseband frequency segmented code.
The correlation process requires that separate storage bins be
provided for each target range and velocity of interest. In
tracking systems, when the target is "range tracked", only a few
range bins need be implemented. In extended range, large angular
coverage surveillance systems, a large number of identical range
bins are required. In such cases the number can be constrained by
directing available processing resources to restricted areas.
Furthermore, a given number of range bins can cover large areas
with relatively coarse resolution and smaller areas with finer
resolution. When used in synthetic aperture applications, a zooming
technique can be implemented wherein available processing resources
can be used to classify designated targets of interest. The
sequential contiguous range bins form an array of coherently
related time elements that can be advantageously processed to
improve operational characteristics. For example, adjacent elements
can be processed together to improve measurement accuracy.
There are several techniques available for obtaining Doppler
information from CFMR; however, a new and novel technique, to be
described, provides correlated range-velocity information from
individual targets in a direct manner.
CFMR signal processing can be accomplished utilizing digital
techniques wherein received signals are converted to baseband
frequencies, quadrature detected relative to the baseband reference
frequency into "I" and "Q" (in phase and quadrature phase)
channels, sampled at a rate related to resolution requirements,
converted from analog to digital signals, and through appropriate
switching correlated into sequential "I" and "Q" storage range
bins. The outputs of the "I" and "Q" range bins sampled at a given
range can be phase rotated sequentially to account for Doppler
shift and are then vectorially added to optimize the signal to
noise ratio of a signal detected at the corresponding range. The
"I" and "Q" outputs corresponding to each input sample are used to
compute the phase angles of the signal vector with respect to the
"I" and "Q" axes. For fixed targets the angle of the vector remains
constant. For moving targets this vector rotates at a rate
corresponding to the Doppler frequency introduced by target's
radial velocity. This is detected by processing the "I" and "Q"
signals through a Fast Fourier Transform (FFT) signal processor or
other phase rotational arrays. This process is coherent and retains
full coherent processing gain.
The following considerations are pertinent:
1. Each frequency segment is a separate entity starting at the time
of its initiation and ending a segment period later. Each is
capable of a separate range reading.
2. In equal time periods, phase changes introduced by Doppler shift
in harmonically related baseband frequencies, which are much lower
than the carrier frequency, are very nearly the same. If required,
a-priori information of the exact frequency of the transmitted
signal defines phase rotation corrections required for aligning
vectors coherently in like Doppler frequency bins.
3. The sampling period for received signals is clocked in
accordance with the transmitted signal format.
4. When receiving signals from fixed targets the phase angle of the
returned signal varies in a known and cyclic manner relative to
target range.
5. Measured range to target is identical for both fixed and moving
targets.
6. When receiving signals from moving targets the phase angle of
the received signal, referenced to the "I" and "Q" axes is a
function of both range and Doppler.
7. Therefore, a measurement of Doppler, and hence, the target's
radial speed, can be derived from a measurement of the progressive
change in the received signal's phase angle with respect to the "I"
and "Q" axes.
To minimize the transmission of harmonics the CFMR waveform is
generally continuous. Changes in the amplitude are minimized. As it
relates to CFMR operation, Doppler shift is simply due to
differences in the transit time to the target that occurs while the
incident wave is being reflected from a moving target. For targets
having closing radial velocities the received pulse is compressed
in time. At the transmitted frequency the received wave is similar,
in terms of continuity, to the transmitted wave. For moving
targets, the converted baseband frequency, relative to the "I" and
"Q" axes, through different angle of rotations than incurred from
fixed target returns or experienced in a replication of the
original transmitted pulsed frequency segment. This continuing
phase rotation is a measurement of the difference in transit time
incurred from reflections off a moving target and provides the
means for measuring the radial velocity of the target. In
harmonically related baseband frequencies of equal pulse periods
the progressive phase shifts are very nearly the same, or can be
phase corrected to be the same, for all frequency segments for all
pulses and provide correlation gain. This change in phase angle can
be measured in several ways. For the digital process previously
described the phase angle is equal to the inverse tangent of the
ratio of "I" and "Q" signals and the rate of phase change or
Doppler frequency is conveniently measured via an FFT
processor.
It is the total management and control of the detailed
characteristics of the transmitted waveform in terms of time,
frequency, phase, amplitude and continuity that when
cross-correlated with target's returned signals provides the means
for simultaneous extraction of detailed target information not
hitherto available from conventional radars. The resolution
characteristics of an extremely wide band pulse compressed radar
can be duplicated and accuracy of measurement improved upon. A
continuous wave, fixed frequency signal, can through appropriate
signal processing, be derived and yield unambiguous velocity
information. The time--bandwidth characteristics of the signals are
efficiently utilized. Peak powers are reduced to average values,
and average powers, when compared to high duty cycle, staggered PRF
radar, are reduced by virtue of reduced eclipsing and time sharing
losses.
The CFMR signal processing technique has direct application in the
design of SONAR systems. Analogs exist between electromagnetic and
sonic sensing systems. They operate in identical domains; time,
frequency and space. Noise and many other operational factors can
be similarly treated. The primary difference exists in
environmental factors related to the mediums such as reverberation,
multi-path, ducting and other transitory variations in the
transmission paths of the energy fields. In medium to long range
SONARS the useful bandwidth can be extremely limited, e.g., less
than 10 Hz. The CFMR signal process utilizes a relatively small
instantaneous bandwidth in each signal channel to provide, over a
period of time, a larger bandwidth for information detail. This
design parameter, along with others that have equal application to
both mediums, make the CFMR signal process extremely useful to
SONAR system application.
The primary object of this invention is to provide a new and useful
radar system wherein the transmitted signal format is a continuous
wave consisting of time programmed, discrete frequency segments and
the frequency separation and stability between selected frequency
segments provides frequency multiplex operation to achieve a
transmit-while-receive capability from a common antenna
aperture.
A second object is to describe a means to extract non-ambiguous
measurement of each target's range and velocity simultaneously from
the same waveform.
A third object is to show that the range bin array of coherent
signal time elements is capable of providing increased measurement
accuracy.
A fourth object is to describe instrumentation required to
implement CFMR.
A fifth object is to describe the design technology involved in the
digitally implemented signal process for extracting range and
velocity information.
BRIEF DESCRIPTION OF THE DRAWINGS
Other objects and many advantages of this invention will become
more apparent upon the reading of the following detailed
description and examination of the drawings, wherein:
FIG. 1 illustrates a transmitted baseband waveform;
FIG. 2 illustrates a pulse compressed waveform;
FIG. 3 illustrates a coherent frequency multiplexed radar receiver
transmitter block diagram;
FIG. 4 illustrates signal commutation into range bins;
FIGS. 5A-5C (hereinafter referred to as FIG. 5), illustrate a range
and Doppler processor functional block diagram; and
FIG. 6 illustrates signal commutation into range bins, digital
version.
FIG. 7 is a schematic demonstrating frequency multiplexing by
digital techniques.
DESCRIPTION OF THE PREFERRED EMBODIMENT
The baseband waveform, refer to FIG. 1, consists of a continuous
waveform of a series of discrete, coherently related, frequencies
having a predetermined segment width and transmitted in a
contiguous manner. The frequency and pulsewidths are chosen in a
pseudo-random manner; however, for the purposes of this discussion
consider a number of linearly stepped, harmonically related,
frequencies of equal pulsewidth wherein: ##EQU1## n.sup.2 =Number
of Range Bins G.sub.pc =N
T.sub.i =WT
Where:
N=The number of frequency segments transmitted in a range code
word.
T=The range code word period.
.SIGMA.BW=Total bandwidth of transmitted signal.
.DELTA.R=Range resolution
BW.sub.n =1 F noise bandwidth
G.sub.pc =Processing gain derived from pulse compression.
.tau.=Pulsewidth of frequency segments
W=The number of rangewords integrated
T.sub.i =Total integration time
c=Velocity of electromagnetic propogation.
To further simplify the discussion, consider four baseband
modulation frequency segments, wherein f.sub.1 =100 kc, f.sub.2
=200 kc, f.sub.3 =300 kc, and f.sub.4 -400 kc, are transmitted
during 10 .mu.s pulse periods 1, 2, 3 and 4 to form a continuous
wave signal, i.e., at the completion of period 4, f.sub.1 is
contiguously transmitted and so on. These baseband frequencies are
to be coherently translated to a desired carrier frequency;
example, a frequency band near 10 GHz. It is important to note that
the baseband frequencies are important and the signal process is
independent of carrier frequency. Parametric values for the chosen
example are:
N=4
G.sub.pc =4
.DELTA.R=375 meters (.apprxeq.0.2 miles)
.SIGMA.BW=400 Khz
BW.sub.n =100 Khz
T=40 .mu.sec
.tau.=10 .mu.sec
Upon reception the returned signals are coherently translated back
to baseband frequencies and through synchronous processing to
account for Doppler frequency rotations, the frequency segments at
each range of interest are separated and effectively time aligned
in parallel such that the voltage maximums can be vectorially added
to form a pulse compressed wave with corresponding processing gain.
The resolution of a uniformly weighted waveform is shown in FIG. 2.
The -11.4 dB minor lobes in the time pattern can be reduced through
appropriate weighing. As N, the number of frequency segmented
pulses are increased, the amplitude of the first minor lobe,
without weighing, approaches -13, dB.
The time minor lobes can be reduced further by continual weighing
techniques wherein the amplitude of the post detected spectral
lines making up the pulse compressed spectrum are tapered from a
central line to opposing ends of the total information bandwidth
prior to the vector summation process.
A simplified block diagram of the CFMR receiver transmitter is
shown in FIG. 3. The transmitting portion of the radar system
consists of items 9, 10 and 11, the reference or clock frequency, a
frequency synthesizer and the transmitter-amplifier. Item 9
provides a stable reference frequency (ex. 100 kHz) to establish a
coherent relationship for all frequencies transmitted; local
oscillator signals or; baseband quadrature detection reference
signals within the receiver; and the clocking source for the signal
processor. The function of the frequency synthesizer, 10, is to
create the various coherent frequencies required. These frequencies
are then combined to form a coherent and contiguous waveform that
is converted upwards to, say, a microwave band of 10.00005 to
10.00045 GHz. The low level signal from the frequency synthesizer
is amplified, 11, and transmitted through circulator 12 to antenna
13 where it is radiated.
A portion of the transmitter power referred to as transmitter
leakage, consisting of power reflected from the antenna mismatch
and that coupled through the circulator, is directed towards the
receiver. A figure of merit for a mixer is its 1 dB compression
point. If subjected to an input power at the 1 dB compression
level, it loses 1 dB of sensitivity. The transmitter leakage power
coupled to the mixer should be less than that value. For very low
power applications this may be achieved by the circulator only;
however, for higher powers a canceller, 14, is required. Its
purpose is to directly couple transmitter power to the summer, 15,
in a negative manner so as to minimize the transmitter leakage
power at the input to the mixer 16.
The received signals inputted to mixer 16 are converted to the
original baseband frequencies, and amplified through I.F. amplifier
17. The frequency bands carrying f.sub.1, f.sub.2, f.sub.3 and
f.sub.4 are next separated one from the other, and from the
transmitting signal being transmitted, through frequency
demultiplexer 18, an I.F. filter array, to separate received
signals into separate frequencies. To prevent adding aliasing noise
into the system, the bandwidth of the demultiplex filters and
following 1F amplifiers, 19, 20, 21 and 22, preceding the phase
detectors are 100 kHz. The isolation required between channels is
dependent upon the specific application. The required isolation is
achieved by multi-section filters. Channelized outputs from the
frequency multiplexer are amplified and frequency converted into
quadrature signals at the original baseband frequencies, f.sub.1,
f.sub.2, f.sub.3, and f.sub.4. The basic components involved
consist of mixers 23 through 30, and quadrature hybrids 31 through
34, inclusive. The coherent local oscillator signal is derived
within the frequency synthesizer and fed into terminal 35 of a
corporate feed that provides coherent signals to the input of the
quadrature hybrids. The "I" and "Q" outputs are fed into filters 36
through 43. The purpose of these filters is to choose the proper
frequency components from their associated mixer circuits. For
example, 1 F amplifier 19 is inputted with the frequency channel
containing f.sub.1, and thus filters 36 and 37 are filters that
pass the f.sub.1 frequency band. On the same basis, filters 38 and
39 pass f.sub.2, 40 and 41, f.sub.3, and 42 and 43, f.sub.4. All
output signals are directed to the signal processor where they are
processed to provide measurements of range and velocity.
It should be noted that during the transmission of the carrier
signal containing, for example f.sub.1, that the transmitter
leakage power is converted and transmitted through the frequency
multiplex channel that receives f.sub.1. Except for limited
applications, f.sub.1 cannot be received during its 10 .mu.sec
transmission period. Signals received at minimum range, 0-1500
meters are blanked. There are a number of places that STC and
blanking controls can be introduced into the circuit. In this
example they are introduced into the gain control circuits of
amplifiers 19, 20, 21 and 22 through inputs 45, 46, 47 and 48,
respectively. The waveform of the control signal is of the same
form for all channels; but is time sequenced in accordance with the
serial format of the transmitted signal.
Processing of CFMR signals for the extraction of pulse-compressed
range and Doppler measurements is conveniently done through digital
logic. The coherent process demands that the spectral
characteristics of the original RF signals be retained and
vectorially added. This is done by the translation of the RF analog
signals to quadrature, digitally coded, signal voltages. A block
diagram illustrating a means of sampling the signals and storing
them in appropriate range bins is shown in FIG. 4. For ease in
presentation, an analog technique for segregating received signals
into coherent pulse compressed range bins is first described. In a
practical case digital techniques will be employed. Design details
as may pertain to the sequence of operation and types of components
involved depend upon the requirements of a specific application and
are directed toward fulfillment of processing requirements with
minimal complexity and cost.
Quadrature components of received signals f.sub.1, f.sub.2, f.sub.3
and f.sub.4 are inputted into the four positions of each section of
coarse range switch 49. To simplify the presentation, three
section, four position switches are described. In addition, only
the in-phase signal process is detailed. The quadrature phase
signals are processed in an identical manner. Furthermore, for
illustration only, a fourth section, section 95, has been added to
the coarse range switch. This section corresponds to range of
0-1500 m and is not normally used. The operation of the coarse
range switch is apparent upon examination of the following
table.
__________________________________________________________________________
Baseband Signal Received* Signal Being SW Sec 50 SW Sec 65 SW Sec
80 SW Sec 95 Transmitted Freq Pos. Freq Pos. Freq Pos. Freq Pos
__________________________________________________________________________
f.sub.2 f.sub.1 52 f.sub.4 67 f.sub.3 82 f.sub.2 97 f.sub.3 f.sub.2
53 f.sub.1 68 f.sub.4 83 f.sub.3 98 f.sub.4 f.sub.3 54 f.sub.2 69
f.sub.1 84 f.sub.4 99 f.sub.1 f.sub.4 51 f.sub.3 66 f.sub.2 81
f.sub.1 96 Time After Transmission 10-20 .mu.s 20-30 .mu.s 30-40
.mu.s 0-10 .mu.s That The Signal is Received* Coarse Range Measured
1500-3000 m 3000-4500 m 4500-6000 m 0-1500 m
__________________________________________________________________________
*Switch operation is delayed by the filter delay and other fixed
circuit delays
In phase baseband signals f.sub.1, f.sub.2, f.sub.3 and f.sub.4
route to positions on each section of the coarse channel switch 49.
Section 50 monitors the signals returned during the period
following their transmission. This corresponds to return from
targets in the 1500 to 3000 meter range; i.e., signal transit
periods of 10 to 20 .mu.s. During the transmission of the pulse
frequency segment referred to as f.sub.2, f.sub.1 is monitored at
section 50 through position 52. During the next pulse period, when
the pulse frequency segment referred to as f.sub.3 is transmitted,
section 50 monitors f.sub.2 through position 53. f.sub.3 and
f.sub.4 are similarly monitored during the next two pulse periods
through positions 54 and 51 of section 50.
Simultaneously and in a sequential manner, section 65 of coarse
range switch 49, is monitoring via positions 67, 68 and 69 and 66,
signal returned during the second period following their
transmission corresponding to targets in the 3000 to 4500 meter
range; i.e., transit periods of 20 to 30 .mu.s. Section 80 is
similarly monitoring signals from target at ranges of 4500 to 6000
meters. For illustration purposes section 95 has been added. It
monitors the following group of pulses in the fourth period after
transmission. In that a four period range code has been chosen for
this example, it is monitoring received signals referenced to the
same baseband frequencies as then being transmitted.
The switching cycle for coarse range switch 49 is 40 microseconds
corresponding to the total code period. It dwells at each contact
for slightly less than 10 microseconds, i.e., the frequency segment
pulse period. The coarse range segmented output, from rotors of
sections 50, 65 and 80, are next routed to analog to digital
converters 55, 70 and 85, respectively.
The range resolution of this system corresponds to a 2.5
microsecond period of 375 meters. The received signals are sampled
a minimum of twice (once each in the I and Q channels) during each
2.5 .mu.s period. Signals from each frequency segment sampled at 10
.mu.s intervals are stored separately within the corresponding
range bins. The input circuit of each analog to digital converter
normally requires a sample and hold circuit; however, in many
applications, tracking A/D converters may be utilized. Samples are
taken at 2.5 .mu.s intervals, e.g., 11.25, 13.75, 16.25, . . .
38.75 .mu.s after their start of transmission. The analog signals,
so sampled, are converted to their digital equivalents, for this
case say 7 bits plus sign, and inputted into the rotors of Fine
Range Switch 100. The analog equivalent of the switch required is
again a three section, four position switch. In this case, only
three sections are illustrated. Requirements for the quadrature
phase signals are identical. Each section of the fine range switch
completes its four position cycle in the 10 .mu.s period of a
frequency segment. As shown, section 56 is monitoring position 57.
It dwells on this position for somewhat less than 2.5 microseconds
during which time the "I" component of signal f.sub.1 is sampled by
the A/D converter 11.25 .mu.s (plus any fixed circuit delays) after
its initial transmission, and stored as a digital word in range bin
62. Ten .mu.s later f.sub.2 is similarly sampled at position 57 and
stored as a second digital word in range bin 62. Progressively, at
10 .mu.s periods, f.sub.3 and f.sub.4 are monitored from position
57 and stored as digital words in range bin 62. The four stored
digital words within the range bin are operated on by the computer
as described later to provide a pulse compressed measurement of
range at 1688 meters.
The other positions of section 56, i.e., 58, 59 and 60, provide
identical functions at later 2.5 .mu.s intervals to store all
consecutively received signals from targets at ranges of 2063, 2400
and 2775 meters, respectively. Sections 71 and 86 through their
respective positions (72, 73, 74 and 75, and 87, 88, 89 and 90)
provide similar functions at 375 meter range intervals from 3188
meters to 5812 meters. This process is completed in 40 .mu.s.
Switches 50 and 100 are implemented with FET or some other solid
state switching matrix. This switching process is repeated W times
for the total integration period and continues for the total
operational period of the radar.
Simultaneously, all consecutive quadrature phase signals are
similarly stored in a parallel group of range bins. For example,
the quadrature phase signals stored in range bin 101 complement the
in-phase signal accumulated in range bin 93. In the following text,
the "I" and "Q" signals so stored will be considered as a single
entity and referred to by the "I" range bin number; i.e., range bin
93.
The individual signal samples corresponding "I" and "Q" signals,
taken a pair at a time, comprise a complex pair of orthogonal
components of phasers which carry the amplitude and phase
information of the received signals at the time the samples were
taken. It is next necessary to process these signals in a coherent
manner and derive pulse compressed range and radial velocity
measurements.
The details of the signal processing to be described subsequently
are shown to demonstrate that their exists at least one method for
extracting the desired information. To those skilled in the art of
radar and signal processing, as is taught for example in August M.
Rihaczek's Principles of High Resolution Radar, copyright 1969 by
McGraw Hill Book Company, it may be obvious that since the wave
form already defined does not exhibit gaps in either the time
domain or in the frequency domain, and is fully coherent, then if
the wave form is processed in a matched filter, which by definition
achieves fully coherent processing, for the wave form to which it
is matched, the following properties can be achieved:
1. The range resolution becomes C/2BW where BW is the total
bandwidth of the coherently processed wave form which for this wave
form is N.
2. The Doppler frequency resolution becomes one over the coherent
integration time which in this case is WT where T is the length per
word and W is the number of words integrated coherently.
3. The full height range ambiguities occur at T if the word is
repeated at intervals of T. These ambiguities may be eliminated if
the sequence is changed from word to word.
4. And finally that, in theory, the unambiguous Doppler frequency
coverage can become virtually that of a single frequency CW wave
form because of the CW and fully coherent nature of the
transmission. In practice, the sampling rate, in this case 1/.tau.,
establishes the range of unambiguous Doppler coverage
capability.
If this is understood, then the particular implementation of a
signal processor to be described in the following paragraphs can
properly be viewed as one of many ways of implementing a matched
filter for the coherent frequency multiplexed radar wave form
previously described.
In fact, the signal processing only has to implement part of the
matched filter function because the filters within the receiver
provide a match to the individual frequency segments. This signal
processing must therefore provide a means for coherently
integrating all the various segments received in the integration
period WT. It must provide this coherent integration for targets at
any range and for any Doppler frequency shift within the design
limits of the system, which in turn are usually less than the
previously quantified maximum unambiguous range and Doppler
capabilities of the system.
The Fast Fourier Transform (FFT) is the basic means to be described
for providing the desired coherent integration. The various
algorithms and hardware implementations of the FFT are well known.
An important point is that if an FFT is performed on K complex
samples uniformly spaced by .tau., then the total unambiguous
frequency coverage is 1/.tau. segregated into K separate bins of
1/K.tau.. Another important point is that the vector rotation and
summation process it performs is fully coherent. The FFT, however,
assumes that all of its samples are of the same waves, for example
a single Doppler frequency. It is shown in a subsequent
mathematical analysis that because of the fact that all the
frequency segments transmitted are coherent and multiples of
1/.tau., that the samples spaced by 1/.tau. manifest only the
Doppler frequency if and only if the sample times and the two way
transit times to the target match within a tolerance determined by
the range resolution of the system, i.e., if and only if the target
is within the range bin being processed. If not, the samples become
scattered and the FFT output is significantly reduced, i.e.,
unmatched. The FFT is capable of providing the required matching
for all Dopplers of interest but only for the range bin being
processed and thus is matched in both range and Doppler. The
processing to be described may be repeated sequentially or
performed in parallel for all range bins of interest.
Since there are WN separate samples to be processed per range bin,
this can be performed in a single FFT of length WN. This is
described as an alternate processing means. First a process is
described wherein the FFT is performed in two sections, one with
FFT's of length W and one with FFT's of length N, and it is shown
that the two processes are equivalent in spite of the very
different implementations. In both processes, only the samples from
a single range bin are analyzed.
In the first process illustrated, these samples are first grouped
by segment frequency. W samples of the same frequency segment occur
at intervals of T. The W samples of the same frequency are analyzed
by a W point FFT. This is done separately for each of the N
different frequencies transmitted. Thus, the total frequency
coverage is 1/T and the frequency resolution is 1/WT.
This is referred to as a fine Doppler bin. It is shown that the
matched output occurs in the same (or common) bin for each of the N
FFT's in this bank of FFT's. A second FFT of N points is then
performed across the N FFT's on the already partially integrated
data in the corresponding output bins. The samples are ordered in
the same order as they were transmitted. Since there are W output
bins in the first bank of FFT's, this process is repeated W
times.
Each time this N point FFT is performed it produces a matched
filter output for the range bin being processed and N Doppler bins
with a total Doppler coverage of 1/.tau. and a Doppler resolution
of 1/N.tau.. This is referred to as a coarse Doppler bin.
The output of this second FFT will not, however, be at its maximum
unless the selected common fine Doppler bin outputs of the first
FFT's are also at their maximum values. This fact can be used to
produce an output within the unambiguous coverage of the coarse FFT
of 1/.tau. and the resolution of the fine FFT or 1/WT. This is
accomplished simply by finding the maximum output in all of the N
bins of the coarse FFT while cycling through the W bins of the fine
FFT and recording which of the common fine Doppler bins was
selected for input to the coarse FFT at the time the maximum output
occurred. This output will be at the maximum possible value (i.e.
fully coherent gain) only if the target return is matched in range
as well as in coarse and fine Doppler. Thus, fully correlated range
and Doppler information is extracted from the same wave form by the
matched filter. The processing and some additional background will
now be described in greater detail.
For fixed targets all NW phasors corresponding to a given range
bin, for example, bin 93, can simply be vectorially summed to
provide a coherent processing gain of NW; i.e. the number of
frequency segments, N, times W, the number of words coherently
integrated. The pulse compressed range resolution is C.tau./2N.
This would constitute matched filtering for fixed targets in range
bin 93, but would not provide matched filtering for moving
targets.
Moving targets introduce a Doppler frequency shift in the received
signals. This causes the phasor corresponding to each subsequent
frequency segment received to be rotated relative to that of a
fixed target return. This phase rotation is dependent upon the
target's radial velocity relative to the radar and the time elapsed
since the first signal received during the integration period being
processed. This progressive phase shift can be systematically
eliminated through progressive counter phase rotations of each
sample phasor corresponding to the Doppler frequency assumed prior
to the vector summation. If the target is in the range bin being
processed and if the actual target Doppler and the assumed Doppler
are the same, the phasors will be colinear and the resultant phasor
or vector will be NW times as large in magnitude as the individual
samples. This results in a coherent processing gain of NW. This can
be best accomplished with digital technology and implementation
and, in particular, it will be shown that an FFT provides the
desired counter-rotations for a number of Doppler bins.
Consider as an example the complex signals stored in range bin 93.
They consist of NW complex signal returns from targets at a range
5063 meters, corresponding to a transit time of 3.75 .mu.s. The "I"
and "Q", 7 bit+sign, are available in serial form for N frequencies
for W receptions. For this example with W=4, there are
2.times.N.times.W or 32 eight bit digital words accumulated and
stored during the WT or 160 .mu.s integration period.
All NW samples for range bin 93 are sequentially routed to computer
102, FIGS. 5A, 5B, and 5C, hereinafter referred to as FIG. 5.
Computer 102 may implement any one of a number of algorithms to
coherently process the samples and extract the range and Doppler
information available in the return signal.
Computer 102 may be a general purpose computer or a special purpose
computer optimized for the application. In the latter case, it may
be implemented to perform a number of the required Fast Fourier
Transform (FFT) algorithms in parallel dependent upon speed
requirements. In the limit, the processing of FIG. 5 may be
replicated for each range bin of interest.
In the case of the linear sweep chosen for this example, the
processing could be greatly simplified. However, non-linear
frequency sequences exhibit numerous advantages over linear ones,
so the processing described will be kept general enough to apply to
the non-linear sequences since no limitation to linear sequences is
intended.
The signals stored in range bin 93 are sequentially routed in the
same order they were received, through bus 140 to Digital
Demultiplexer 141, under the control of Timing and Control 142. The
latter is synchronized by the clock and sync bus 182 from the
reference frequency source of FIG. 3. For example, for N=4 TI
Demultiplexer SN 74LS155 could be used (refer to page 7-175 of
reference 1--"The TTL Data Book for Design Engineers", 2nd Edition,
Texas Instruments, Incorporated). Bus 143 carries the A and B
select signals changing at period .tau.. Inputs 1 and 2 also occur
at period .tau.. The 1c and 2c lines are the "I" and "Q" samples
respectively. The output lines feed busses 147-148. The control
function is to route W signal returns from like frequency segments
to their designated FFT (Fast Fourier Transform). For the case of
the linear sequency f.sub.1 is received 4 times and routed at 40
.mu.s intervals via bus 147 to f.sub.1 FFT 146.
An FFT can be thought of as first taking the phasors represented by
the sampled complex input data and, on a bin by bin basis,
counter-rotating each subsequent phasor by a phase angle which is
proportional to the frequency of the bin times the time elapsed
from the first sample and then vectorially summing the resulting
phasors. The complex sum is referred to as the output of the bin.
Each output bin corresponds to a Doppler frequency band or Doppler
bin. The total Doppler frequency range covered by the FFT is the
reciprocal of the sampling period T: or, for this case, 25 KHz,
since T=40 microseconds. The FFT processes a number of bins which
is equal to the number of samples taken, W. The Doppler resolution
is thus 6.25 KHz for W=4. The taking of an FFT is a fully coherent
process and the improvement in signal to noise ratio is W. Also, it
will become important later to note that if a single frequency
lying exactly at the center of one of the FFT bins is analyzed by
an FFT the output in that bin is at the angle of the first phasor,
because all the W-1 subsequent phasors are counter rotated to
exactly that same angle.
The results of the f.sub.1 FFT are stored within f.sub.1 FFT 146
double buffered memory. The same signal processing applies for each
of N frequency segments f.sub.2 through f.sub.n. These tasks may be
performed concurrently or sequentially depending on the
implementation of Computer 102. In this implementation, the
frequency word samples f.sub.2, f.sub.3, and f.sub.4 are processed
in parallel. For example, the f.sub.4 samples are routed via bus
148 to f.sub.n FFT 149. The FFTs are clocked at .tau. intervals via
bus 150 from Timing and Control 142. For real time operation, these
FFTs must be completed within the time period WT (160 .mu.s) and
then be ready to process the whole new set of samples from the next
integration period which are stored in the FFT's double buffered
memory while the current integration period is being processed. The
characteristics of the outputs stored in FFT 146-149 are now
examined. The signals inputted to Computer 102 were mixed down to
baseband frequencies f.sub.1 through f.sub.n. The corresponding
received signals are:
where
f.sub.r =frequency of received signals
f.sub.n =baseband frequencies
f.sub.d =Doppler frequency
but
where:
K=an integer from 1 to N
.DELTA.f=frequency step
and
where:
.tau.=duration of a frequency segment
The samples are taken at period of
The phase rotation between samples, .phi..sub.r, to f.sub.n alone
is:
but fron 2) and 3)
and 5) become ##EQU2## K and N are both integers and the phase
change between samples is an integer number of 2 rotations which is
indistinguishable from no rotation at all. Thus, each FFT sorts
input signals (f.sub.n +f.sub.d) into its respective output bins as
if the sample to sample changes were due to f.sub.d alone, i.e.,
all FFT's have their maximum signal outputs in the same numerical
output storage bin.
Since the outputs of all the FFTs at the differing f.sub.n.sup.s
are enhanced in the same bin, corresponding to f.sub.d, it is
possible to add the outputs of the FFTs in the corresponding bins
incoherently. The information obtained is similar to that obtained
from a group of pulse Doppler radars operating at a PRF of T.
Range resolution, .DELTA.R, and Doppler resolution .DELTA.f.sub.d :
##EQU3##
Ambiguities: R.sub.amb and f.sub.d amb ##EQU4##
Processing Gain, (G.sub.p) ##EQU5##
Neither the full bandwidth nor high sampling rate available from
the CFMR implemented system has been utilized. The continuing
objectives of the CFMR process are:
1. To utilize the total transmitted energy in a coherent manner to
achieve fully coherent gain.
2. To obtain range resolution corresponding to the full bandwidth
transmitted.
3. To eliminate Doppler ambiguities associated with the 1/T
sampling rate.
As described earlier, the phase of the output of the FFT bin, which
is at a frequency corresponding to f.sub.D, is equal to the phase
of the first input sample to the FFT (phase scattering due to noise
is neglected for this discussion, but the presence of noise does
not alter the processing to be described which is linear and fully
coherent). The phase relationships between these first phasors from
each of these N coherent frequencies are critical to the subsequent
processing.
The phase of a received signal return from a given target relative
to that of a stable L.O. at f.sub.c is a function of the frequency
(f.sub.c +f.sub.n) of the transmitted segment and the round trip
transit time td.sub.n. The transmitted signals and the L.O. are all
coherent to one another. This can be achieved, and is in this
example, by having all frequency segments sent in phase at time
zero; i.e., at their instant of initial transmission. (In a general
case, it is sufficient to have all phases known.) The L.O. signal,
V.sub.LO, can be expressed as a function of time, t, as:
where
v.sub.LO is the maximum amplitude of the voltage vector
.phi..sub.O is an arbitrary phase angle
The transmitted signal, V.sub.T, can be similarly expressed as:
Since (f.sub.c +f.sub.n) is transmitted (n-1) integer units of
.tau. after the transmission of (f.sub.c +f.sub.l) and f.sub.n is a
multiple of 1/.tau., refer to equation 6), and f.sub.c is equally
constrained, then the term (n-1).tau. represents the time required
for an integer number of phase revolutions of 2.pi. and can thus be
dropped from further consideration in matters of determining phase
differences.
Since phase changes associated with phase reversal upon reflection
and miscellaneous fixed delays can be accounted for and eliminated
from the subsequent analyses, the return signal V.sub.Rx can be
written:
At the sample time, ts.sub.n, i.e., t=ts.sub.n, the phase
difference between the return signal 10) and the L.O. 8) is:
Simplifying:
The first term is a function of the baseband frequency, f.sub.n and
the range sampling error (ts.sub.n -td.sub.n). The last term is the
number of carrier wave lengths to the target and back.
Equation 12) can be rearranged:
The change in phase, .DELTA..phi., between frequencies (f.sub.c
+f.sub.(n+1)) and (f.sub.c +f.sub.n) is found by substracting
.phi..sub.n from .phi..sub.(n+1).
The change in td is zero for fixed targets, but for moving targets,
the range to the target and therefore the transit time to the
target has changed and:
Where .DELTA.td is the sample to sample transit time difference
introduced by a target with constant radial velocity. The
transmissions are spaced by .pi.,therefore
But f.sub.(n+1) is an integer multiple of 1/.tau.. The first phase
related term of equation 14) (f.sub.(n+1) ts.sub.(n+1)) thus
becomes
where K is an integer. K can be dropped from phase calculations
since it produces an integer multiple of 2.pi.. With the
understanding that all values of t.sub.s are spaced by .tau., the
subscript n can now be dropped from ts.sub.n. This feature and
equation 15) modifies equation 14) to:
expanding, re-arranging, and cancelling:
The differential phase shifts involved in the FFT process can all
be referenced to the return from the baseband frequency f.sub.1.
Then td.sub.1 is the two way transit time for the initial f.sub.c
+f.sub.1 transmission. For the constant radial velocity case:
substituting 20) into 19) , cancelling and rearranging:
Providing:
then the right hand term of 21) reduces to
and
.DELTA..phi. is a linear combination of two terms. The first term
is the frequency difference between adjacent baseband frequency
segments, .DELTA.f, times the difference between the target transit
time td.sub.1 and the nearest sample time ts. If ts=td.sub.1, this
term vanishes. When td.sub.1 .noteq.ts, this term scatters values
of .DELTA..phi. by an amount which depends upon the sequence of
transmissions. For linear steps, cross coupling exists between
range and velocity phase shifts. Systems of greatest interest have
non-linear sequences and the readings are scattered when td.sub.1
.noteq.ts. Thus when the target is centered in the range bin of
interest, only the second term is significant. The second term is
the segment to segment phase shift due to the target's radial
motion between samples (i.e., Doppler frequency shift).
Thus, in conclusion, if the target is outside the range bin being
analyzed, the phase shifts are scattered whereas if the target is
centered in the range bin being analyzed, then even though the
segments are at different (but coherent) frequencies, the segment
to segment phase shifts are due only to the single Doppler
frequency, just as if the transmission were at a single CW
frequency. Recalling that the phase of the output of the FFT bin
corresponding to the true target Doppler is equal to the phase of
the first input sample, this is of extreme importance, since the
resulting constant segment to segment phase shifts are readily
extracted by a second FFT.
To achieve the CFMR objectives outlined previously, a second FFT is
performed in a sequential manner across common Doppler frequency
output bins of the N FFT's 146 through 149. It is permissable to
use the outputs of these FFT's because, as described previously,
the phases of the FFT Doppler bin outputs into which the target
falls are the same as that of the first sample of each f.sub.n. The
results are:
1. The signal to noise ratio is further enhanced by the factor
N;
2. The full bandwidth of the transmission is utilized in fully
coherent processing and thus the range resolution is increased to
C.tau./2N, i.e. pulse compressed range information becomes
available; and
3. The unambiguous Doppler capability is increased from 1/T=1/NT to
1/.tau..
When the output of one set of common fine Doppler frequency bins
has been completely processed and appropriately stored, a second
set is processed. This process is continued until all W common
Doppler frequency bins have been processed sequentially on a bin by
bin basis.
The first fine Doppler frequency bin of the f.sub.1 FFT appearing
on complex output of the bus 151 is routed by Digital Multiplexer
152 to its output bus 153, then on through Digital Multiplexer 158
to FFT 161. Digital Multiplexer 152 is the digital equivalent of a
"W" way analog switch that for this example is implemented for W=4.
TI Multiplexer, part number SN 74LS 153 (page 165, reference 1),
may be used for W=4. The devices can be cascaded for larger values
of W. It is controlled by bus 154. Its function is to step through
inputs 151 through 162, sequentially outputting them to bus 153.
The other FFT's in this group are similarly output to their
respective busses; for example, f.sub.n FFT 149 outputs 156-63 are
sequentially output through bus 157. The outputs are inputted to
Digital Multiplexer 158. This multiplexer is the digital equivalent
of a "N" way analog switch that, for this example, is implemented
for N=4 (again, TI part number SN 74LS153 can be used). It is
controlled by frequency select bus 158. Its function is to
sequentially cycle through the N outputs from the common Doppler
frequency bin outputs of f.sub.1 FFT 146 through f.sub.n FFT 149
and input them sequentially into FFT 161 in the order of
transmission. Note that Digital Multiplexer 158 steps through all N
of its positions before Digital Multiplexers 152 through 155 step
to the next common Doppler bin. FFT 161 thus receives N inputs from
a given Doppler frequency bin, performs an N point FFT and stores
the results in N course Doppler frequency bins 188 through 189.
This is repeated for each of the W separate common Doppler bins.
FFT 161 is operated by control bus 187. All timing sequences
generated by timing and control unit 142 are synchronized via clock
and sync bus 182 from frequency reference 9 of FIG. 3.
If the sequence of transmission is sufficiently non linear, and
td.sub.1 .noteq.ts the second FFT will produce a minimal output. If
the outputs of the first FFT are present in bin 1 of the first
group of FFTs and td.sub.1 =ts, the second FFT will produce an
output in its bin corresponding to the target Doppler. If the
outputs of the first FFT are present in bin 1 but td.sub.1
.noteq.ts and the transmission sequence is sufficiently non linear,
the second FFT will again produce only a minimal output. If the
target is within bin 93, there will always be a sample point ts
within .+-..tau./2N of td.sub.1, in which case, the sampling error
term introduces a maximum loss of 3.9 dE in the vector summation
performed by the second FFT. This corresponds to a range resolution
of C.tau./2N. It may be noted that the 3.9 dB maximum loss can be
reduced to less than 1 dB by doubling the sample rate. In our
example, i.e., for N=4, the maximum loss is 3.7 dB and doubling the
sample rate can reduce them to 0.86 dB.
Bin 1 of the first group of FFTs when taken on the data in range
bin 93 thus comprises a filter matched to the range bin and Doppler
frequency of FFT bin 1. There are W bins in the first group of
FFTs. The process may then be performed for bin 2 of the first
group of FFTs, etc. All of the W output bins of the first group of
FFTs are examined so that finally samples corresponding to bin W on
bus 162 of the f.sub.1 FFT through bin W on bus 163 of the f.sub.N
FFT appear sequentially on bus 160 for analysis by the FFT 161.
Note that FFT 161 under the control of timing unit 142 must perform
W separate N point complex FFT's in the time period WT. Thus, the
average time available to complete each FFT is T, which in this
example is 40 .mu.s. This is well within the present state of the
art. The samples on bus 160 are analyzed in order of transmission,
so that a constant radial velocity target produces a constant
segment to segment phase change, i.e., a constant Doppler
frequency, in the input data to FFT 161. This combination of FFTs
implements the equivalent of a bank of matched Doppler filters
which is matched to the target only if the target is in the range
bin being analyzed, in this case range bin 93.
The total processing gain is NW; that is the signal-to-noise ratio
at the output of the second FFT 161 is improved by a factor of WN
when compared to range bin 93's input to Computer 102.
Additionally, the total bandwidth of the transmitted signal has now
been coherently utilized resulting in a pulse compressed range
resolution of C.tau./2N. At the output of FFT 161, the unambiguous
Doppler coverage is 1/.tau. as desired, however, the Doppler
resolution is 1/T, not the desired 1/WT. It remains to show how the
outputs of the fine and coarse FFT's are correlated so that the
full Doppler resolution available in the waveform can be
utilized.
To summarize, the first group of FFTs have a sampling rate of T and
a processing period of TW; thus, overall bandwidth=1/T or, in this
example, 1/T, ex. 25 KHz i.e., Doppler frequency ambiguities
@1/T
Doppler frequency resolution =1/WT, ex. 6.25 KHz
The second FFT has a sampling period of .tau. and a processing
period of N.tau.; thus, overall bandwidth=1/.tau. or, in this
example, 100 KHz i.e., Doppler frequency ambiguities @1/.tau.
Doppler frequency resolution=1/N.tau. or 1/T, ex.25 KHz.
The first group of FFT's (146 to 149) provides the fine Doppler
resolution but the readings are ambiguous at the inverse of their
lower sampling rate 1/T. The second FFT extended the ambiguities to
the inverse of their higher sample rate (1/.tau.); but provides a
reduced resolution. The objective now is to pair these readings
such that the fine Doppler readings are unambiguous out to the
sampling rate of the processor. This is accomplished in the
following manner.
The basic approach utilizes the fact that the W fine or common
Doppler bin outputs of the N fine FFT's must be sequentially
stepped through, as previously described, so that for each step the
N signals are provided as inputs to the second or coarse FFT. At
each of these steps the N outputs of the second or coarse FFT are
scanned at a rate such that all N outputs are examined before the
next fine input step occurs. In this manner, a total of NW coarse
FFT output combinations, each corresponding to a fine Doppler bin,
are sequentially examined. Then to find the correct Doppler bin
for, for example, the single largest target in the range bin, it is
sufficient to merely simultaneously record (via latch 168 in the
following description) both the bin number of the fine or common
Doppler bin being input to the coarse FFT at the time of occurrence
of the largest output for all the NW combinations examined and the
bin number of the coarse FFT in which that maximum output occurred.
The complex FFT outputs are converted to magnitudes and compared
within Magnitude Comparator 167. One input to the Comparator is the
coarse FFT output then being examined while the other input is the
largest level signal found up to that point (or just a threshold at
the beginning of a sweep). When a larger signal is found,
Comparator 167 strobes the latch 168 which stores the coarse and
fine Doppler bin numbers as well as other pertinent information.
This new signal, stored in complex form by latch 168, then becomes
the B (reference) input to Comparator 167. Thus, after all NW
combinations are examined, i.e., at the end of a sweep. Latch 168
contains the coarse and fine Doppler bin information and other
correlated data for the single largest target in the range bin.
Then Arithmetic Unit 175 manipulates the coarse and fine Doppler
bin information stored in latch 168 to produce the composite
Doppler bin information.
For simplification, consider instrumentation for positive Doppler
frequencies only. Then the true Doppler frequency, f.sub.d, can be
found from the reading, f.sub.d1, obtained from the first group of
FFT's and the corresponding Doppler bin number, J, from the second
FFT as follows:
where
f.sub.d =true Doppler frequency
f.sub.d1 =Doppler frequency reading obtained from 1st group of
FFT
K=1 or 2, as will be described
J=an integer from 1 through N
In this case J is just the bin number of the second FFT. The
ambiguities in the first FFT's Doppler readings are separated by 1
and the bins of the second FFT are 1 apart so that the second FFT's
reading permits the true Doppler value to be selected from the N
possible ambiguities.
This simplified approach is utilized in FIG. 5, although no loss of
generality is intended. A serial process is depicted although
parallel ones could be implemented if speed requirements so
dictated. The outputs of FFT 161 appearing on busses 188 through
189 are scanned by Digital Multiplexer 165 to sequentially select
one of the N input busses and route it to its output bus 166 where
it is provided as input A to Comparator 167. Each FFT process
performed by the f.sub.2 FFT is completed in T .mu.sec and there
are N output bins. The serial process to be described must be
completed, under the control of Timing and Control Unit 142 via bus
176 in T/N=.tau.=10 .mu.s. Digital Multiplexer 165 is implemented
in the same manner as N way Digital Multiplexer 158. Bus 166 also
carries the data to Latch 168 where it can be stored along with
other correlated information derived simultaneously from the same
input data as may be commanded by Comparator 167. Digital
Multiplexer 165 has two additional sections controlled by bus 176,
wired so that the inputs correspond to one bin above and one bin
below the bin of interest. Where one of these bins is outside the
range of 1 to N, the input is hard wired to a zero amplitude. These
additional outputs of Digital Multiplexer 165, called upper and
lower bin are also routed to Latch 168 on busses 186 and 183,
respectively. This information is required to facilitate
association of the coarse and fine velocity bin information within
Arithmetic Unit 175. The latched value, corresponding to the input
on 166 at the time Latch 168 was strobed, appears on bus 169 and is
provided as the "B" input to Comparator 167. Comparator 167
converts the "I" and "Q" components of both the "A" and "B" inputs
to magnitudes M.sub.A &M.sub.B, respectively, where
This may be accomplished using a table lookup or any of the other
well known approximations. Comparator 167 compares M.sub.A with
M.sub.B. (This can be implemented by using TI 4 bit magnitude
comparators P/N SN 74LS85 (page 7-57 of Reference 1) cascaded as
shown on page 7-64 of Reference 1.) If the magnitude of "A" is
greater than the magnitude of "B" at the time the strobe signal (at
.tau. periods of) from Timing and Control Unit 142 via line 170
appears, an output is provided on line 171 to cause Latch 168 to
latch its inputs. (Latch 168 can be implemented using a bank of TI
octal "D" type edge triggered, tri-state, flip flops, PN SN
74LS364, page 7-467 of Reference 1). A method for automatically
finding the single largest target in the range bin is described to
demonstrate that all the information in the output is
correlated.
At the start of processing for each new range bin, the outputs on
bus 169 are set to the value provided from Timing and Control Unit
142 via bus 172 thereby establishing a desired prescheduled level
for the magnitude threshold. Simultaneously, the "target present
flag" on line 173 is reset to "0" by a reset signal from bus 172.
This is accomplished by having two of the tri-state latches with
outputs tied together in standard bus fashion to bus 169. One of
the latches is fed by threshold bus 172 and that latch's outputs is
only enabled when the "target present flag" is a logic "0". Any
time Latch 168 is strobed by line 171, logic "1" on line 174 is
latched and forces the "target present flag" line 173 to logic "1".
This also enables the other latches' outputs to bus 169 and the
outputs from the latch containing the initial threshold are
disabled. Only if the incoming signal exceeds threshold will the
"target present flag" go to a logic "1" to indicate the presence of
valid data on the remaining outputs of Latch 168 and Arithmetic
Unit 175. The first time this occurs the value of the signal from
bus 166 which exceeded the preset threshold value becomes the input
to Comparator 167. Unless a signal appears that exceeds the new and
higher threshold, this remains for the period the given range bin
is processed. When a signal larger in magnitude than the new
threshold is examined, it in turn becomes the new threshold. In
this way comparator 167 locates and defines the largest signal in
the range bin, which is then simultaneously latched into bus
169.
Consider that instant of time the last A>B strobe occurs on line
171. This occurs when the largest signal is in the range bin. At
that instant, Digital Multiplexer 165 under control of Timing and
Control Unit 142 via bus 176 has selected that one of N bins of FFT
161 having largest output. Bus 176 is input to latch 168 and is
latched to become the coarse Doppler bin number on bus 177.
Simultaneously, the N Digital Multiplexers 152 through 155 were
controlled by bus 154 to select one of the W fine Doppler bins. It
follows that the fine Doppler bin selected is the one that caused
FFT 161 to produce its largest output. The bus 154 information is
therefore latched by Latch 168 to become the fine Doppler data on
bus 178. Timing and Control Unit 142 also provides Latch 168 with
the Range Bin Address via Bus 179. The latched output is the range
bin information provided to Bus 180.
Note that the outputs of the first group of FFTs, 146 through 149
were never looked at directly since the signal-to-noise ratio is
improved only by a factor of W at this point. Instead, the output
of FFT 161, where the signal-to-signal noise ratio is improved by a
factor of NW, is monitored. This yields the best possible
statistical decision as to fine Doppler value since the signal to
noise ratio is maximum at this point. Since one and only one fine
Doppler bin is selected at a time by Multiplexers 152 through 155,
the fine resolution (1/WT) is obtained.
The latched Coarse and Fine Doppler information on Busses 177 and
178, respectively, are processed within Arithmetic Unit 175 to
yield the final Doppler output on Bus 181. With the simplifying
assumption that only positive Doppler velocities are instrumented,
the Arithmetic Unit 175 merely adds J-k units of 1/T to the fine
Doppler reading. J is the coarse Doppler bin, out of a possible N
values, input on Bus 177. k is either 1 or 2 depending on the ratio
of the amplitudes of the signals in the adjacent upper (U) and
lower (L) coarse velocity bins appearing on busses 184 and 185,
respectively. Arithmetic Unit 175 performs magnitude comparisons on
complex ("I" & "Q") data. If U>L, then k=1. If U<L, then
k=2. If U=L, then k=1 if the f.sub.d1 reading corresponds a bin
number.ltoreq.W/2 out of the first group of FFTs and 2 otherwise.
These comparisons can be implemented using the means similar to
those described for magnitude Comparator 167. A digital adder can
be implemented using a bank of TI P/N SN 74LS283 4 bit binary full
adders (page 7-415 of Reference 1) with one input being the Fine
Doppler information from Bus 178 and the other input being the
output of a ROM look up table with at least N entries. The ROM is
addressed by the J input from bus 177 and the calculated k value.
Each ROM output is the pre-calculated product of (J-k) and 1/T.
All the output information on Busses 169, 173, along with the range
word, 180 and the Doppler words 181 is derived at the same instant
of time from the same data and all applies only to the largest
magnitude target in the range bin and is therefore totally
correlated.
A single FFT of length NW operating with the same NW samples, would
yield identical outputs. This is mentioned to illustrate the fact
that the details of the processing scheme do not affect the outputs
of the process as long as a matched filter is implemented for every
range velocity combination of interest. This also leads to the
conclusion that the transmit sequence could be permutted during the
period of integration without altering the output in the bin
containing the target; but of course the ambiguity function would
be affected. In fact, as a matter of design choice, the sequence
could be varied from word to word randomly or pseudorandomly, or in
any other desired manner to obtain some desired characteristic of
the ambiguity function. In practice, filters 36 through 43 of FIG.
3 would typically not be ideal matched filters, but would have a
response which would be a matter of design choice relating to
isolation requirements, the effects on the system ambiguity
function, etc. The processing scheme illustrated was chosen for
several reasons.
(1) It was judged to be a better vehicle than the single FFT
approach for teaching insight into the process of implementing a
matched filter for this class of waveforms.
(2) It has the property that the number of multiplications or
multiplies required to perform the FFT (and hence usually the
corresponding processing time) can be reduced. The number of
multiplications required to perform a FFT of length N is often
given in the literature as N log.sub.2 N. A single FFT of length NW
would require NW log.sub.2 NW or (log.sub.2 W+log.sub.2 N)
multiplications. The scheme illustrated required N (W log.sub.2
W)+W (N log.sub.2 N) or NW (log.sub.2 W+log.sub.2 N)
multiplications which is as might be expected the same as themethod
using the single FFT.
However, the scheme illustrated is capable of significant
(hardware/processing time) reductions when multiple adjacent range
bins are to be implemented. For example, if the N range bins with a
segment .tau. were instrumented, then instead of repeating the
first groups of N FFTs, N times, it would suffice to perform the
first group of N FFTs once as illustrated then perform N separate
rotations of the outputs of the existing first group of FFTs. Since
each FFT in the first group is dedicated by frequency, and the
phase shift and the time delay are related if the frequency is
known, each of the N phase rotations of the data on bus 153, for
example, could be made to correspond to a different sampling point.
Typically, these would be spaced by .tau./N or the time width of a
range bin. Of course, there would have to be corresponding
rotations on the corresponding other N-1 busses through 157.
An approximation to the reduction in the number of multiplies
required through using this technique can be obtained by
recognizing that a phase rotation of a complex number requires two
multiplies per component or four total per rotation. Since there
are a total NW samples to be rotated by N different phase shifts,
this operation requires 4N.sup.2 W multiplies. The second FFT must
be performed NW times and the N.sup.2 W log.sub.2 N+4 N.sup.2 W
multiplies are required altogether, i.e, the total number of
multiplies required is N.sup.2 W (log.sub.2 N+4). If N separate
FFTs of length W were performed, the number of multiplies required
would be N (NW log.sub.2 NW) which is N.sup.2 W (log.sub.2
N+log.sub.2 W). The savings accrue when log.sub.2 W>4 or
W>16. The savings available is N.sup.2 W(log.sub.2 W-4)
multiplies which may be very significant for large W. One skilled
in the art might be led to recognize that commonalities in the
input data can be taken advantage of to effect even more
significant reductions in the processing time/hardware
required.
Range ambiguities occur if the range word is periodically repeated.
In CFMR this type of periodocity can be avoided by transmitting the
frequency segments making up each range word in a non repetitive
manner and continuing to do so in all successive transmissions. To
be effective N>32. This provides a thumbtack ambiguity function.
Under such conditions, the CFMR processing objectives enumerated on
page 13 have been met;
Resolution (.DELTA.R and .DELTA.f.sub.d) ##EQU6##
Ambiguities (R.sub.amb and f.sub.d amb) ##EQU7##
Processing Gain (G.sub.p)
FIG. 4 provides an analog technique for sorting signals into range
bins. A digital implementation integrated within Computer 102 is
preferred. FIG. 5 and the accompanying description made primary
reference to a single range bin, 93. FIG. 6 depicts a simplified
digital implementation of the range processor of FIG. 4. The
process is readily extended for operation with any higher value of
N. Here the bulk of the commutation is performed within the
internal addressing decoding logic of a RAM (Random Access Memory).
Tracking A/D converters 110 through 117 provide continuous digital
representations (ex.: 7 bits+sign) of their analog inputs
consisting of "I" and "Q" components of the received signals
f.sub.1 through f.sub.4. The parallel digital outputs of the
tracking A/D converters are strobed into their dedicated latches,
118 through 125 simultaneously at .tau./N. For this example:
##EQU8##
Appropriate synchronization of clock functions are derived from
sync Bus 182. (This .tau./N period corresponds to the times when
the A/D converters of FIG. 4 were strobed. The dedicated latch
outputs are sequentially multiplexed onto data bus 126 at
.tau./2N.sup.2 =0.3125 .mu.sec per latch under the control of
multiplexer control bus, 133. As a result, the "I" sample word
followed by the complementary "Q" sample word for each of N
frequencies appears serially on bus 126 and is fed into CPU
(central processing units) 127. CPU 127 reads the contents of data
bus 126 each 0.3125 .mu.sec. and via RAM address bus 131 addresses
locations within RAM 130 each .tau./4N.sup.2 =0.15625 .mu.sec. The
same data is written into two range bins. The most significant
portions of the overall address correspond to "I" and "Q" samples
of the same frequency segment for the same range bin and therefore
repeat every T=40 .mu.sec period. Since the address changes every
.tau./4N.sup.2, the basic address pattern is ##EQU9## steps in
length. It is generated within the synchronous counter 132
synchronized to bus 182. Counter 132 can be part of the Timing and
Control Unit 142 of FIG. 5. A number of address sequences can be
utilized to assure that the signals are properly routed. For
example, the address is broken into 4 portions corresponding to the
preceding descriptions of the commutations of FIG. 4, plus an
accumulator flag portion described in a subsequent paragraph.
"I"-"Q" portion of address:
1 bit at .tau./2N.sup.2 =0.3125 .mu.sec per state
Fine Range portion of address:
2 bits binary upcount at .tau./N=2.5 .mu.sec per state
Coarse Range portion of address:
2 bits binary downcount at rate .tau./N.sup.2 =0.625 .mu.sec per
state with 1 downcount inhibited at end of period.
Note: FIG. 4 and 6 both represent all range devices, thus samples
taken simultaneously of consecutively transmitted segments
correspond to targets exactly one coarse range (.tau. .mu.sec)
apart. At every fine range sample time (at interval of .tau./N)
there are exactly N samples taken simultaneously corresponding to
the N coarse ranges. In FIG. 4, the bank of coarse range switches
need only change position once each .tau. due to the parallelism of
the implementation. In FIG. 6, the N different coarse samples taken
simultaneously every .tau./N must be multiplexed sequentially onto
the same line and thus the coarse range portion of the address
changes every .tau./N.sup.2 seconds. The coarse range address
change is inhibited once every .tau.. This corresponds to the
change in position of the bank of coarse range switches in FIG. 4.
Thus, the samples are always tagged with the correct coarse range
bin number.
The remaining section of the address allows the samples to be
stored separately:
these less significant portions of the address determine the
storage location within the range bin and change every .tau./N
.mu.sec and consist of two subportions.
log.sub.2 W bits (where the number of words integrated, W, is a
power of 2) , indicating the word number within the bin. This is 2
bits for W=4
log.sub.2 N bits (where the number, N, of unique frequency segments
transmitted is a power of 2), indicating the transmission location
within the word. This is 2 bits for N=4 as in our example.
At the beginning of the range word all counts are synchronized from
bus 182. The portions of RAM address bus 131 of interest are
derived from the counter address bus 134. All latch (118 to 125)
sequences are clocked from bus 137 to mutually exclusively enable
each of the latches 118 through 125 for a 0.3125 .mu.sec period.
Counter 132 provides a synchronized 8 line output on multiplexer
control bus 133. Each of the 8 outputs is routed to one of the
tri-state latches 118 through 125. Counter 132 also provides timing
and control signals, 138, to CPU 127 to synchronize the entire
range processor.
CPU 127, via bus 129, stores the contents of data bus 126 at the
selected address, i.e., a location within the appropriate range
bin. Thus, the samples of the various returned "I" and "Q"
frequency segments f.sub.1 through f.sub.4 are stored separately in
the proper sequence within the correct range bins of RAM 130. Since
the data on bus 126 changes half as frequently as the RAM address
on bus 131, the new data is added to the contents of two separate
range bins, corresponding to whether the accumulator flag bit
portion of RAM address bus 134 is a logic 1 or 0. This optional
feature, provided for scanning systems, starts a second
accumulation at the midpoint in time of the first accumulation.
When an accumulation is completed, the contents of the range bin
are output for further analysis and a new accumulation is begun.
CPU 127 reads the data in RAM 130 on a range bin by range bin
basis. The data appears on Data Bus 129 and is routed to output bus
140 for input to the processing associated with FIG. 5.
Alternately, bus 140 can feed a multiplexer so that the data from
separate range bins are routed separately to a number of
processors, each as depicted in FIG. 5, for parallel
processing.
A single A/D converter operating at 0.3125 .mu.sec per conversion
installed on bus 126 obviates the need for separate tracking A/D
converters 110 through 117. These can be replaced by sample and
hold circuits. Also, latches 118 through 125 can be replaced by
analog multiplexers.
It should also be evident that the sampling times used in the
processing described above can be advanced or delayed in accordance
with the range determination made by Computer 102 to cause range
bins defined by the samples to track the location of a target. Each
target to be tracked requires a movable (or selectable) pair of
sample points, repeated at the period .tau.. Two range bins per
tracked target are adequate. The movable and fixed samples can be
taken on a non-interfering basis to provide a track-while-scan
capability. A simple implementation for tracking a large number of
targets is to have fixed array of such samples with outputs of the
appropriate pairs routed to their respective range bins. In a
general case, the samples used for the all range processor can be
used for the tracking, adding only those range bins required for
tracking a given number of targets.
Referring back to FIG. 5, it should be noted that the circuit can
be implemented with STC (Sensitivity Time Control) or Doppler
discrimination such as responding to moving target only. The
variable threshold on Bus 172 can be adjusted to instrument STC in
the receiver; primarily, to maximize dynamic range, and also
Doppler discrimination if it were varied as a function of the
Doppler bin being processed at that time. To accomplish this,
Timing and Control Unit 142 would, via Bus 172, causes Latch 168 to
be initialized to an appropriate threshold level just prior to the
time that each new velocity bin is processed. For maximum
desensitization of certain Doppler bins, it is feasible to simply
bypass processing these bins entirely. Multiplies targets in the
same range bin, but having different velocities, are all reported
individually. This follows from the fact that all the transmission,
reception and processing functions described are linear and that
therefore superposition applies. Accordingly, if multiple targets
existed within the same range bin, but had sufficiently different
velocities, they appear in separate velocity bins. Each time a
target exceeds its combined range/velocity bin threshold, all
correlated information is caught by latch 168 and eventually appear
on Busses 169, 173, 180 and 181. The "Target Present Flag" on bus
173 can initiate storage of these potentially larger number of
outputs in secondary memories to allow further processing.
In general, the correlated range, velocity and signal level
information can be output from Computer 102 as is or stored for
further processing within Computer 102 depending on the intended
application. For example, it is possible to derive an interpolated
range reading by examining the outputs of adjacent range bins. If
adjacent bin signals were of equal amplitude and at the same
velocity, this would imply that the true target is located halfway
between the range bin values. Similarly, if in a single range bin,
outputs of equal amplitude were found in adjacent velocity bins,
this implies that the true velocity is halfway between the velocity
bin values. In general, the amplitude ratio of signal in adjacent
range bins at a given velocity determines the interpolated range
value. Similarly, the amplitude ratio of signals in adjacent
velocity bins at a given range determines the interpolated velocity
value.
Further processing can also be used to improve the detectability of
small targets in the presence of larger ones through recognition
that once the largest target is found, its predicted trails in
other range/velocity bins can be evaluated.
In certain applications, for example, missile guidance, it is
desirable to track the target into zero range. Under such
conditions the signal-to-noise ratio available is orders of
magnitude greater than required for detection, but the frequency
segment then being transmitted becomes self jamming. If the
reflected transmitted power is reduced to a level that does not
introduce excessive non-linearities into the receiver circuits,
then Doppler filtering is adequate to separate received signals
from the transmitted signal and reception continues into zero
range. For medium to high power applications, power management is
utilized wherein the transmitted power is reduced as the range to
target is decreased. The magnitude of the transmitted power is
established as required to maintain a predetermined signal-to-noise
ratio within the receiver process.
The available processing resources, as depicted by FIG. 4, can be
used for range zooming wherein the range resolution is improved for
targets within a portion of the total range being observed. To
improve the range resolution by a factor of 12, the signal format
can be changed as follows: ##EQU10##
The pulse frequency segments are a continuing multiple of the
highest baseband frequency previously used; i.e., 400, 800, . . .
4800 KHz. These baseband frequencies are translated to the carrier
band of interest. On reception the signals are mixed down to I.F.
demultiplexer level where the larger bandwidths require new
multiplexing circuits. Through judiciary choice of local oscillator
frequency and circuit time sharing, the resources of the remaining
circuitry can be advantageously utilized. A 2.5 .mu.s period
centered at the specific range of interest is to be divided into
twelve parts. To achieve this, the switching rates in both the
coarse and fine range circuits are increased twelvefold. Each range
bin now correlates signals in 31 meter range increments. The total
resources of the signal process are now focused in specific areas
of interest at the expense of temporary discontinuance of the
surveillance mode of operation.
In standard CFMR operation, the overall bandwidth is N .DELTA.f,
where N is the number of unique frequency segments to be
transmitted and .DELTA.f is the separation between any one of the
transmitted frequencies and the next highest or lowest transmitted
frequency.
In some applications, it may be necessary or desirable to spread
the spectrum of the transmission. For example, the probability of
an external receiver, that does not have the means to perform a
coherent signal process on the CFMR signal receptions, detecting
the CFMR signals is reduced when the bandwidth of the CFMR
transmission is spread. The spectrum is spread by introducing a
number, M, of guard channel frequency offsets in the transmissions.
The frequency offsets are generally large compared to N.DELTA.f but
are not necessarily uniform.
These offsets are introduced on a time multiplexed basis such that
a continuous transmission results. Refer to FIG. 3. The offsets are
introduced in any desired order by Frequency Synthesizer 10. This
involves heterodyning one of the M guard channel frequencies at an
I.F. level. All N frequency segments making up a given range word
are transmitted on a common guard channel. A following range word
is sent on a different (perhaps randomly chosen) guard channel. On
reception the guard channel steps are removed. The local oscillator
signal generated in the frequency synthesizer 10 and routed to
Mixer 16 carries the time programmed frequency offsets required to
subtract out each successive guard channel frequency.
The returns are stored and processed separately on a guard channel
by guard channel basis and stored. These separate output signals
agree as to target range and velocity. They may be incoherently
added together to achieve an improvement in signal-to-noise ratio
and accrue the benefits of frequency diverse transmissions.
The larger bandwidth provided by coherent guard channel frequency
spreading produces a number of very fine range lobes that are
encompassed within the broader pulse compressed range lobe. Such
characteristics may be advantageously used. For targets with a
small depth in comparison with the basic pulse compressed
resolution, an improved signal-to-noise ratio is realized at the
ranges where the returns reinforce. At such ranges, range
resolution is improved to correspond to a time equal to the
reciprocal of the new overall transmission bandwidth. For some
applications, range bins may be instrumented only for those ranges
so that the signal to clutter ratio is maximum by virtue of the
high resolution capability at these known ranges. Targets with a
radial velocity relative to the radar can be expected to walk into
one of the instrumented range bins. Complex targets of greater
physical depth relative to the new range bin might have individual
characteristics that satisfy small depth requirements and provide
fine signal information capable of assisting in target
identification.
As previously discussed, Doppler ambiguities exist at the inverse
ratio of the sampling rate of 1/.tau. utilized by FFT 161.
For that example:
where
f.sub.d max=maximum non-ambiguous Doppler frequency=1/10.sup.-5
=0.1 MHz
f.sub.c =carrier frequency (10 GHz)
V=target velocity
C=speed of light 3.times.10.sup.8 m/sec.
Solving for v ##EQU11##
Targets with radial velocities above 1500 m/sec. can fold over, or
alias with lower speed targets and are ambiguous.
CFMR is a continuous wave signal and, if required, the unambiguous
Doppler capabilities may be extended by utilizing higher sampling
rates than 1/.tau.. Where the unambiguous Doppler frequency
bandwidth capability is increased, the Doppler frequency shift
involved may exceed the receiver's minimum bandwidth and
appropriate implementation is required.
In order to provide for the processing of any number of the total
N.sup.2 range bins available, the process described in FIG. 5 may
be repeated sequentially, range bin by range bin or in parallel
through the use of additional sets of FFTs operating in
parallel.
The same technique may be used to process returns in a single range
resolution cell (bin) or in all range bins or any intermediate
number of bins and thereby implement a single target tracking
processor to an all range surveillance receiver processor.
Naturally, the circuitry ahead of the processor can be further
simplified if only a small number of range bins are to be
implemented. It is also true that if a large number of range bins
are implemented, then, commonalities in the input data can be taken
advantage of to reduce the total number of computations required,
thereby improving the processing speed or reducing the total amount
of hardware required in the processor, Computer 102.
FIG. 3 depicted analog filtering for separating baseband
frequencies f.sub.1, f.sub.2, f.sub.3 and f.sub.4. Time sampling
techniques can also be utilized to achieve frequency filtering.
This is referred to as Time Domain Filtering. Since the transmitter
signal and receiver local oscillator signals are precisely known
and contained within the same radar unit, it is possible to sample
received signals when the transmitter feed through signal is zero.
The techniques for accomplishing this is shown in FIG. 7.
Assuming f.sub.1 is the signal whose detection is desired, it can
be heterodyned in mixer 200 with a local oscillator whose frequency
is also f.sub.1. The DC output 205 is a replica of the f.sub.1
frequency segment pulse of duration .tau.. A matched filter for
this pulse is comprised of an integrator 203 in combination with a
time delayed negative feedback signal 202. It provides the
autocorrelation function of the pulse of length .tau. to which it
is matched wherein the output pulse builds up from a zero value at
time (t.sub.s -.tau.) to a value of .tau. at time t.sub.s and then
the negatively fed back time delay signal subtracts from the stored
signal to again establish a zero value at the time (t.sub.s
+.tau.), curve 206. This signal, if sampled at t.sub.s, is sampled
at maximum voltage value.
All other signals, including the undesired transmitter leakage
signal input into the first mixer along with the desired f.sub.1
signal, are harmonically related to 1/.tau.; i.e., they are integer
multiples of 1/.tau.=f.sub.1 and the output is in the form of beat
notes containing a integer number of cycles. The integrated output
of the "I" channel (sine wave) is an offset cosine wave, curve 207,
having a phase reversal at the zero crossover coincident with
sample time t.sub.s. The integrated output of the "Q" channel
(cosine wave) is a sine wave, curve 208, having a phase reversal at
zero crossover also coincident with sample time t.sub.s. The
important relationship is that both the "I" and "Q" channels beat
notes go through zero at the sample time. The number of cycles
within the sample period .tau. is a function of the beat frequency
difference. The maximum amplitude of the beat frequency signal is
inversely proportional to the number of cycles involved; thus, the
slope of the curve going through the zero point is the same for all
beat frequencies involved. Both the local oscillator and the
transmitted signal are within the control of the system so that the
zero crossover point can be effectively controlled, and all
signals, except the desired one are efficiently rejected.
The position of the D-C integrated signal is dependent upon the
transit time to target. The sample times are implemented a period
.tau. apart. The response of the adjacent range cell is shown
dotted in 206. If the target lies exactly halfway between the two
sampling points, t.sub.s -.tau./2, the signal loss is 6 dB. The
average filter loss is 2.5 dB. This compares to an average filter
loss for conventional radars of 1.8 dB. In the final design, this
can be accepted or, through additional logic, reduced.
It is readily apparent to those skilled in the art that the details
of the frequency-segmented signal format, in terms of number of
pulses utilized, frequency sequence, bandwidth and other related
design parameters, along with the sequence of digital operation,
circuit techniques, etc., are matters of design choice chosen in
accordance with specific applications involved. Changes,
modifications, and improvements to the above described embodiment
of this invention may be made by those skilled in the art without
departing from the spirit and scope of the invention. In view of
the many changes, modifications, and implementations that may be
made to the above described embodiment of this invention without
departing from the spirit and scope of the invention, we do not
wish the patent to be limited in any manner inconsistent with the
invention as defined in the appended claims.
* * * * *